**2. Material and methods**

It is essential to control the diameter tolerance of annular fuel for actualizing dual cooled fuel. Therefore, a comprehensive calculation of the optimal dimensions and array of annular fuel rods for a VVER-1000 is applied based on the moderator to fuel ratio, fuel rod pitch, and annular heat surface area to reference. Furthermore, some thermal–hydraulic limitations are considered to achieve a suitable configuration for the annular fuel rods. The annular-8 configuration is nominated as the most promising configuration based on fully thermal–hydraulic analysis and neutronic research [19].

There are 163 fuel assemblies in the core of the VVER-1000 reactor. It has been arranged in a hexagonal lattice with a lattice pitch of 23.6 cm. There are 311 fuel rods, 18 guiding channels for control rods and/or burnable absorber rods (BARs), and a central channel in each fuel assembly. **Figure 2** shows the arrangement of the fuel assembly [26].

**Figure 2.** *The arrangement of fuel assembly [14, 15].*

*The Effect of Al2O3 Concentration in Annular Fuels for a Typical VVER-1000 Core DOI: http://dx.doi.org/10.5772/intechopen.105192*

**Table 1** presents significant specifications for the core of the VVER-1000 reactor.

The typical layout of a fuel assembly for the annular case with 8 8 arrays is demonstrated in **Figure 3**. There are 156 fuel rods and 12 guiding channels for control rods in each fuel assembly [20].

**Table 2** shows the details of the designed values of the annular fuel which have been calculated by Mozafari (2013) [20]. The MNCP5 and COBRA-EN codes were used to find many neutronics and thermo-hydraulics core parameters.

In the present study, the geometry is drawn with GAMBIT software. GAMBIT offers a concise and powerful set of solid modeling-based geometry tools. If you already employ a CAD package, GAMBIT runs both the geometry import and "cleanup" functions that you'll require. Top down geometry construction using 3D primitives without the complexity of a full-fledged CAD package allows you to create geometries fast. Different CFD problems need different mesh types, and GAMBIT gives you all the options you need in a single package.

In this study, triangular cells are employed to generate the meshes. The number of computational cells is 1.01 million. **Figure 4** displays the quality of the mesh in the fuel rod.

FLUENT reads the generated mesh using GAMBIT. FLUENT is the world's largest commercial Computational Fluid Dynamics (CFD) software. FLUENT is a Green-Gauss Finite Volume Method with a Cell-Centered formulation. The major point is the finite volume method (FVM).


**Table 1.**

*VVER-1000 reactor specifications [15].*

#### **Figure 3.**

*The fuel assembly layout of annular pins and equivalent lattice cell [8].*


#### **Table 2.**

*Dimensions of the Annular-8 fuel rods [8].*

The same boundary conditions, such as heat flux, outlet pressure, inlet temperature, and mass flow rate, are considered for nanofluids and pure water. The boundary conditions for the inlet of the fuel assembly, temperature, *T*<sup>0</sup> = 561 K and profiles of uniform axial velocity,*u*<sup>0</sup> are set. The non-slip conditions are considered for the fuel rod wall. The rate of 1.753 kg/m.s is considered for the net flow in the fuel assembly. Pressure is set at 15.7 MPa during reactor operation.

*q* ¼ *qmax* cosð Þ *π*z*=*L is the axial heat-generation distribution, where *q*, *z*, and *L* are the volumetric heat-generation, the axial length, and the active fuel rod length, respectively. To define the cosine function, it is written in the C programming language and compiled in FLUENT.

The governing equations of the nanofluid for the conservation of mass, momentum, and energy in a steady state are written below [27, 28]:

$$\nabla \cdot \left( \rho\_{\eta^f} \mathbf{V} \right) = \mathbf{0} \tag{1}$$

*The Effect of Al2O3 Concentration in Annular Fuels for a Typical VVER-1000 Core DOI: http://dx.doi.org/10.5772/intechopen.105192*

**Figure 4.** *The quality of mesh in the fuel rod.*

$$
\nabla \cdot \left( \rho\_{\eta f} \mathbf{V} \mathbf{V} \right) = -\nabla p + \nabla \cdot \mathbf{r} \tag{2}
$$

$$\nabla \cdot \left(\rho\_{\eta f} \text{Ve}\right) = -\nabla \cdot \left(k\_{\eta f} \nabla T\right) - \nabla \cdot \left(p \, V\right) + \nabla \cdot \left(\tau \, V\right) \tag{3}$$

Where *ρ* is the density of the nanofluid, *V* is the velocity vector, *p* is the pressure, *τ* is the stress tensor, *e* is the specific total energy, and *T* is the temperature. *knf* is the conductivity of the nanofluid.

The CFD is used to solve the denoted Navier–Stokes equations. In this code, the SIMPLEC (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm, a modified form of the SIMPLE algorithm, is used for numerical procedures in CFD. The algorithm manipulates the same steps as the SIMPLE algorithm with a minor change in the momentum equations, allowing the SIMPLEC velocity correction equations to delete fewer important expressions than those deleted in SIMPLE. It tries to avoid the effects of reducing dropping velocity neighbor correction terms.
